Sam Jelbart

Dr Sam Jelbart

Lecturer

School of Computer and Mathematical Sciences

Faculty of Sciences, Engineering and Technology

I am an applied mathematician with a background in the analysis of dynamical systems characterised by multiple time-scales and abrupt transitions. The use of geometric methods is a common theme in my research.

I have expertise in the analysis of ordinary differential equations and non-smooth systems, but a broader interest in the dynamics of maps, partial differential equations and non-autonomous systems. More recently I have been working on rigorous geometric approaches to model reduction in complex dynamical systems with applications in systems biology.

My research is aimed at understanding the behaviour of applied dynamical systems, with a particular emphasis on identifying and utilising structure associated with multiple scales and/or the loss of smoothness. A lot of my research is driven by a long term goal to develop and apply rigorous geometric methods to the study of complex systems, with an eye towards understanding the dynamics of problems of high social and scientific significance in, e.g., climate, biological and biophysical systems.

My PhD focused on planar but highly 'singular' dynamical systems, where I developed expertise in Geometric Singular Perturbation Theory and a method of desingularisation known as geometric blow-up. During my time as a postdoc in Munich and Vienna, I applied this knowledge to dynamical systems with more than two time-scales (both generally and in the context of models for intracellular calcium oscillations), discrete dynamical systems, partial differential equations and non-autonomous systems.

More recently, I have been interested in the development and application of novel geometric methods to the study of complex dynamical processes arising in the study of gene regulatory networks and other models in systems biology.

  • Journals
    Year Citation
    2024 Jelbart, S., & Kuehn, C. (2024). Extending discrete geometric singular perturbation theory to non-hyperbolic points. Nonlinearity, 37(10), 49 pages.
    DOI
    2024 Jelbart, S. (2024). Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast Systems. SIAM Journal on Applied Dynamical Systems, 23(3), 1836-1869.
    DOI
    2024 Jelbart, S., Kuehn, C., & Kuntz, S. V. (2024). Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems. Journal of Nonlinear Science, 34(1), 68 pages.
    DOI Scopus1
    2023 Jelbart, S., & Kuehn, C. (2023). DISCRETE GEOMETRIC SINGULAR PERTURBATION THEORY. Discrete and Continuous Dynamical Systems- Series A, 43(1), 57-120.
    DOI Scopus7
    2022 Jelbart, S., Pages, N., Kirk, V., Sneyd, J., & Wechselberger, M. (2022). Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics. SIAM Journal on Applied Dynamical Systems, 21(2), 982-1029.
    DOI Scopus4
    2022 Jelbart, S., Kristiansen, K. U., Szmolyan, P., & Wechselberger, M. (2022). Singularly Perturbed Oscillators with Exponential Nonlinearities. Journal of Dynamics and Differential Equations, 34(3), 1823-1875.
    DOI Scopus5
    2021 Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly perturbed boundary-focus bifurcations. Journal of Differential Equations, 296, 412-492.
    DOI Scopus10
    2021 Jelbart, S. (2021). BEYOND SLOW-FAST: RELAXATION OSCILLATIONS in SINGULARLY PERTURBED NONSMOOTH SYSTEMS. Bulletin of the Australian Mathematical Society, 104(2), 342-343.
    DOI
    2021 Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly perturbed boundary-equilibrium bifurcations. Nonlinearity, 34(11), 7371-7414.
    DOI Scopus9
    2020 Jelbart, S., & Wechselberger, M. (2020). Two-stroke relaxation oscillators. Nonlinearity, 33(5), 2364-2408.
    DOI Scopus21

  • Conference Papers
    Year Citation
    2024 Jelbart, S., & Kuehn, C. (2024). A formal geometric blow-up method for pattern forming systems. In Contemporary Mathematics Vol. 806 (pp. 49-86). American Mathematical Society.
    DOI

  • Preprint
    Year Citation
    2024 Jelbart, S. (2024). Rate and Bifurcation Induced Transitions in Asymptotically Slow-Fast
    Systems.
    2024 Jelbart, S., Kuehn, C., & Sánchez, A. M. (2024). Characterising exchange of stability in scalar reaction-diffusion
    equations via geometric blow-up.
    2024 Jelbart, S., Kristiansen, K. U., & Szmolyan, P. (2024). Travelling Waves and Exponential Nonlinearities in the
    Zeldovich-Frank-Kamenetskii Equation.
    2024 Rahmani, B., Jelbart, S., Kirk, V., & Sneyd, J. (2024). Understanding broad-spike oscillations in a model of intracellular
    calcium dynamics.
    2023 Jelbart, S., & Kuehn, C. (2023). A Formal Geometric Blow-up Method for Pattern Forming Systems.
    2023 Jelbart, S., & Kuehn, C. (2023). Extending Discrete Geometric Singular Perturbation Theory to
    Non-Hyperbolic Points.
    2022 Hummel, F., Jelbart, S., & Kuehn, C. (2022). Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg
    equation.
    2022 Kuntz, S. -V., Jelbart, S., & Kuehn, C. (2022). Geometric Blow-up for Folded Limit Cycle Manifolds in Three Time-Scale Systems.
    DOI
    2022 Jelbart, S., & Kuehn, C. (2022). Discrete Geometric Singular Perturbation Theory.
    2021 Jelbart, S., Pages, N., Kirk, V., Sneyd, J., & Wechselberger, M. (2021). Process-Oriented Geometric Singular Perturbation Theory and Calcium
    Dynamics.
    2021 Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2021). Singularly Perturbed Boundary-Equilibrium Bifurcations.
    2020 Jelbart, S., Kristiansen, K. U., & Wechselberger, M. (2020). Singularly Perturbed Boundary-Focus Bifurcations.
    2019 Jelbart, S., Kristiansen, K. U., Szmolyan, P., & Wechselberger, M. (2019). Singularly Perturbed Oscillators with Exponential Nonlinearities.
    2019 Jelbart, S., & Wechselberger, M. (2019). Two-Stroke Relaxation Oscillators.

I was awarded a prestigious Marie Curie Fellowship to work on the project Model Reduction for Complex Systems with Exponential Nonlinearity via Geometric Singular Perturbation Theory https://cordis.europa.eu/project/id/101103827. The fellowship is valued at just under 200,000 Euro over two years.

  • Position: Lecturer
  • Phone: 83135006
  • Email: sam.jelbart@adelaide.edu.au
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor Level Seven
  • Room: 7.42
  • Org Unit: School of Computer and Mathematical Sciences
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